# Full text of "Treatise On Analysis Vol-Ii"

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```xii       NOTATION

H(a)                                             entropy  of a  finite partition a:  13.9,

Problem 27

H(a//?)                                          entropy of a finite partition a relative to

w                                                 a finite partition ft: 13.9, Problem 27

V ty > aiv • • • v a«                       least upper bound of a finite sequence of

y==1                                               finite partitions: 13.9, Problem 27

h(u, a)                                           entropy of a mapping w relative to a

finite partition a: 13.9, Problem 28

h(u)                                              entropy of a mapping u: 13.9, Problem 28

J f </ju, J f(jc) d/*(*)                          integral of a vector-valued function: 13.10

.Sfc(X, /*), JS?c(/0* «^c                     sPace   of complex-valued  ju-integrable

functions: 13.10

NjX/)                                   J* |/| 4*: 13.11

Na(/)                                 (J* I/I2*)172: 13.11

^|(X, /i), .S?R(/*), JS?2                     space   of  (finite)   real-valued   square-

integrable functions: 13.11

N                                                space of ^-negligible functions: 13.11

L|(X, fi)9 LfOu), Lg                        space of classes of pth power integrable

functions: 13.11 and 13.11, Problem 12

N//)                                   Np(/) for any/in the class/: 13.11

&c(X, /O, -^c(^)> «^c                     space  of complex-valued square-integ-

rable functions: 13.11
Lc(X, /z), LcOu), LC                        space   of   classes   of   complex-valued

square-integrable functions: 13.11
M^C/), mn(f)9
ess sup/(^), ess inff(x)              maximum and minimum in measure off:

xeX                   JceX                                 i o 10

^H (X, /x), -S^R (M), ^R                    space of real-valued ju-measurable func-

tions bounded in measure: 13.12
J?c (X, /*), jSfc (M)J «^c                   space of complex-valued /i-measurable

functions bounded in measure: 13.12

, fj)9 L£(f<i), Lg                         space of classes of real-valued ^-measur-

able functions bounded in measure: 13.12

(X, ju), Lc'Gw), LC°                      space of classes of complex-valued /*-

measurable     functions    bounded     in
measure: 13.12
, //)                                        space of (finite) real-valued //-measurable

functions: 13.12, Problem 2

S(X, n)                                         space of classes of (finite) real-valued /z-

measurable functions: 13.12, Problem 2```